Towards a Nano Geometry? Geometry and Dynamics on Nano Scale

TL;DR

This paper explores the unique geometry and dynamics at the nanoscale in cell physiology, contrasting it with classical mechanics and quantum theories, and discusses mathematical challenges in biological and nanomedical applications.

Contribution

It applies Gelfand's distinction to nanoscale biological systems, highlighting the need for specialized mathematical frameworks for intracellular dynamics.

Findings

Insights into mesoscale geometry and dynamics in cell physiology

Identification of mathematical challenges in nanoscale biological modeling

Discussion of non-invasive control of magnetic nanoparticles

Abstract

This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elaborated - in contrast to the familiar Newtonian mechanics and the more recent, but by now also rather well established quantum field theories. Examples are given originating from the systems biology of insulin secreting pancreatic beta-cells and the mathematical challenges of an envisioned non-invasive control of magnetic nanoparticles.